Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


## NULL


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SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta1_pelagic 2 1.683993
beta0_pelagic 2 1.454430
beta2_yellow 3 1.436856
beta2_pelagic 2 1.436578
beta1_black 1 1.414334
beta0_yellow 1 1.236037
beta1_pH 7 1.212300
beta1_yellow 4 1.205360
parameter n badRhat_avg
beta2_pH 2 1.202580
beta0_black 1 1.183017
beta3_yellow 1 1.174098
tau_beta0_yellow 1 1.142947
tau_beta0_pelagic 1 1.118450
tau_beta0_pH 1 1.118232
beta0_pH 1 1.112149
Table 2. Summary of unconverged parameters by area
afognak BSAI CI eastside NG NSEI NSEO PWSI PWSO SOKO2SAP WKMA
beta0_black 0 0 0 0 0 1 0 0 0 0 0
beta0_pelagic 0 0 0 0 0 0 0 1 1 0 0
beta0_pH 0 0 0 0 0 0 0 1 0 0 0
beta0_yellow 0 0 0 0 1 0 0 0 0 0 0
beta1_black 0 0 0 0 0 1 0 0 0 0 0
beta1_pelagic 0 0 0 0 0 0 0 1 1 0 0
beta1_pH 1 1 0 1 0 0 0 1 1 1 0
beta1_yellow 1 0 1 0 1 0 0 0 0 0 1
beta2_pelagic 0 0 0 0 0 0 0 1 1 0 0
beta2_pH 0 0 0 0 0 0 0 0 0 0 1
beta2_yellow 0 0 1 0 1 0 0 1 0 0 0
beta3_yellow 0 0 0 0 0 0 1 0 0 0 0
tau_beta0_pelagic 0 0 1 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 0 0 1 0 0 0 0 0 0
tau_beta0_yellow 0 0 1 0 0 0 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.124 0.073 -0.257 -0.128 0.028
mu_bc_H[2] -0.096 0.045 -0.173 -0.100 0.001
mu_bc_H[3] -0.435 0.070 -0.573 -0.433 -0.295
mu_bc_H[4] -0.987 0.195 -1.368 -0.980 -0.599
mu_bc_H[5] 0.868 0.942 -0.155 0.682 3.034
mu_bc_H[6] -2.169 0.311 -2.752 -2.175 -1.547
mu_bc_H[7] -0.446 0.107 -0.667 -0.442 -0.239
mu_bc_H[8] 0.241 0.397 -0.356 0.206 1.089
mu_bc_H[9] -0.287 0.136 -0.558 -0.287 -0.017
mu_bc_H[10] -0.100 0.069 -0.228 -0.102 0.039
mu_bc_H[11] -0.123 0.038 -0.199 -0.124 -0.049
mu_bc_H[12] -0.254 0.103 -0.474 -0.251 -0.052
mu_bc_H[13] -0.135 0.076 -0.281 -0.136 0.022
mu_bc_H[14] -0.303 0.098 -0.511 -0.300 -0.118
mu_bc_H[15] -0.344 0.050 -0.441 -0.344 -0.244
mu_bc_H[16] -0.250 0.402 -0.908 -0.287 0.570
mu_bc_R[1] 1.361 0.148 1.076 1.362 1.654
mu_bc_R[2] 1.453 0.093 1.267 1.454 1.638
mu_bc_R[3] 1.395 0.142 1.121 1.396 1.677
mu_bc_R[4] 0.909 0.205 0.470 0.918 1.285
mu_bc_R[5] 1.214 0.454 0.317 1.220 2.115
mu_bc_R[6] -1.586 0.401 -2.376 -1.580 -0.803
mu_bc_R[7] 0.258 0.178 -0.102 0.259 0.603
mu_bc_R[8] 0.537 0.183 0.167 0.538 0.887
mu_bc_R[9] 0.303 0.207 -0.137 0.320 0.663
mu_bc_R[10] 1.246 0.165 0.907 1.256 1.562
mu_bc_R[11] 1.043 0.097 0.853 1.040 1.229
mu_bc_R[12] 0.826 0.207 0.418 0.826 1.237
mu_bc_R[13] 1.030 0.104 0.823 1.031 1.224
mu_bc_R[14] 0.896 0.146 0.602 0.899 1.177
mu_bc_R[15] 0.781 0.112 0.562 0.781 1.002
mu_bc_R[16] 1.092 0.127 0.845 1.095 1.332
tau_pH[1] 5.178 0.448 4.321 5.163 6.083
tau_pH[2] 2.025 0.225 1.624 2.012 2.519
tau_pH[3] 2.245 0.221 1.837 2.237 2.700
beta0_pH[1,1] 0.550 0.180 0.179 0.558 0.892
beta0_pH[2,1] 1.359 0.176 0.998 1.360 1.693
beta0_pH[3,1] 1.425 0.191 1.025 1.438 1.762
beta0_pH[4,1] 1.567 0.212 1.123 1.580 1.954
beta0_pH[5,1] -0.853 0.281 -1.456 -0.830 -0.359
beta0_pH[6,1] -0.655 0.425 -1.701 -0.591 -0.012
beta0_pH[7,1] -0.425 0.439 -1.345 -0.416 0.493
beta0_pH[8,1] -0.661 0.281 -1.294 -0.624 -0.203
beta0_pH[9,1] -0.640 0.294 -1.266 -0.615 -0.149
beta0_pH[10,1] 0.360 0.208 -0.089 0.380 0.720
beta0_pH[11,1] -0.084 0.163 -0.413 -0.080 0.222
beta0_pH[12,1] 0.480 0.189 0.096 0.480 0.849
beta0_pH[13,1] 0.008 0.143 -0.274 0.009 0.292
beta0_pH[14,1] -0.315 0.167 -0.662 -0.310 0.008
beta0_pH[15,1] -0.027 0.189 -0.415 -0.027 0.335
beta0_pH[16,1] -0.470 0.348 -1.280 -0.414 0.054
beta0_pH[1,2] 2.797 0.167 2.447 2.804 3.097
beta0_pH[2,2] 2.874 0.136 2.602 2.872 3.140
beta0_pH[3,2] 3.051 0.271 2.281 3.098 3.433
beta0_pH[4,2] 2.935 0.139 2.654 2.940 3.203
beta0_pH[5,2] 4.734 1.426 2.956 4.399 8.221
beta0_pH[6,2] 3.116 0.212 2.701 3.119 3.528
beta0_pH[7,2] 1.977 0.172 1.649 1.976 2.325
beta0_pH[8,2] 2.872 0.176 2.522 2.874 3.220
beta0_pH[9,2] 3.436 0.224 3.022 3.433 3.882
beta0_pH[10,2] 3.737 0.203 3.331 3.740 4.153
beta0_pH[11,2] -4.855 0.296 -5.433 -4.858 -4.295
beta0_pH[12,2] -4.787 0.396 -5.602 -4.779 -4.030
beta0_pH[13,2] -4.572 0.420 -5.377 -4.587 -3.728
beta0_pH[14,2] -5.631 0.484 -6.638 -5.618 -4.773
beta0_pH[15,2] -4.297 0.336 -4.974 -4.304 -3.623
beta0_pH[16,2] -4.860 0.398 -5.644 -4.847 -4.104
beta0_pH[1,3] 0.880 0.473 -0.323 0.986 1.521
beta0_pH[2,3] 2.199 0.157 1.892 2.198 2.501
beta0_pH[3,3] 2.518 0.149 2.228 2.516 2.808
beta0_pH[4,3] 2.961 0.160 2.642 2.959 3.278
beta0_pH[5,3] 1.436 1.744 -1.221 1.187 5.450
beta0_pH[6,3] -0.497 1.012 -2.259 -0.654 1.549
beta0_pH[7,3] -2.070 0.639 -3.509 -2.002 -0.996
beta0_pH[8,3] 0.288 0.194 -0.102 0.285 0.665
beta0_pH[9,3] -0.751 0.593 -2.407 -0.596 -0.031
beta0_pH[10,3] 0.293 0.805 -1.901 0.550 1.238
beta0_pH[11,3] -0.106 0.332 -0.721 -0.116 0.568
beta0_pH[12,3] -0.866 0.355 -1.628 -0.834 -0.252
beta0_pH[13,3] -0.117 0.309 -0.715 -0.127 0.505
beta0_pH[14,3] -0.255 0.261 -0.775 -0.255 0.273
beta0_pH[15,3] -0.697 0.302 -1.312 -0.681 -0.124
beta0_pH[16,3] -0.392 0.279 -0.937 -0.391 0.146
beta1_pH[1,1] 3.049 0.320 2.453 3.031 3.708
beta1_pH[2,1] 2.166 0.271 1.674 2.150 2.749
beta1_pH[3,1] 1.975 0.307 1.454 1.952 2.669
beta1_pH[4,1] 2.389 0.334 1.825 2.361 3.143
beta1_pH[5,1] 2.280 0.347 1.724 2.252 3.106
beta1_pH[6,1] 3.804 1.058 2.285 3.580 6.328
beta1_pH[7,1] 2.569 0.855 0.852 2.533 4.382
beta1_pH[8,1] 3.915 0.889 2.619 3.720 6.122
beta1_pH[9,1] 2.335 0.415 1.707 2.292 3.265
beta1_pH[10,1] 2.177 0.285 1.687 2.156 2.812
beta1_pH[11,1] 3.259 0.207 2.858 3.254 3.681
beta1_pH[12,1] 2.558 0.222 2.128 2.553 3.000
beta1_pH[13,1] 2.966 0.212 2.557 2.963 3.406
beta1_pH[14,1] 3.417 0.219 3.012 3.411 3.857
beta1_pH[15,1] 2.530 0.233 2.084 2.529 2.985
beta1_pH[16,1] 4.094 0.639 3.171 3.984 5.590
beta1_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,2] 0.141 0.382 0.000 0.000 1.370
beta1_pH[4,2] 0.036 0.392 0.000 0.000 0.076
beta1_pH[5,2] 0.001 0.013 0.000 0.000 0.005
beta1_pH[6,2] 0.021 0.181 0.000 0.000 0.014
beta1_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[8,2] 0.001 0.016 0.000 0.000 0.004
beta1_pH[9,2] 0.004 0.063 0.000 0.000 0.003
beta1_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta1_pH[11,2] 6.699 0.331 6.061 6.699 7.325
beta1_pH[12,2] 6.464 0.465 5.622 6.440 7.421
beta1_pH[13,2] 6.954 0.454 6.055 6.955 7.826
beta1_pH[14,2] 7.268 0.498 6.364 7.246 8.298
beta1_pH[15,2] 6.771 0.369 6.066 6.775 7.502
beta1_pH[16,2] 7.450 0.437 6.599 7.444 8.295
beta1_pH[1,3] 2.376 0.941 1.222 2.163 4.852
beta1_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta1_pH[5,3] 3.679 7.364 0.989 2.895 9.187
beta1_pH[6,3] 2.470 1.076 0.616 2.443 4.329
beta1_pH[7,3] 2.919 0.646 1.849 2.848 4.375
beta1_pH[8,3] 2.758 0.357 2.078 2.750 3.493
beta1_pH[9,3] 2.812 0.596 1.993 2.688 4.427
beta1_pH[10,3] 3.075 0.869 2.005 2.835 5.376
beta1_pH[11,3] 2.696 0.385 1.967 2.698 3.458
beta1_pH[12,3] 4.120 0.434 3.332 4.100 5.019
beta1_pH[13,3] 1.699 0.334 1.024 1.706 2.352
beta1_pH[14,3] 2.516 0.340 1.857 2.513 3.179
beta1_pH[15,3] 1.977 0.324 1.364 1.965 2.641
beta1_pH[16,3] 1.803 0.313 1.188 1.805 2.402
beta2_pH[1,1] 0.486 0.127 0.294 0.467 0.792
beta2_pH[2,1] 0.568 0.339 0.249 0.509 1.239
beta2_pH[3,1] 0.648 0.472 0.224 0.550 1.600
beta2_pH[4,1] 0.478 0.208 0.219 0.445 0.905
beta2_pH[5,1] 1.430 0.952 0.252 1.279 3.793
beta2_pH[6,1] 0.186 0.065 0.091 0.176 0.341
beta2_pH[7,1] 0.019 0.578 0.000 0.000 0.062
beta2_pH[8,1] 0.245 0.085 0.127 0.230 0.442
beta2_pH[9,1] 0.424 0.213 0.170 0.383 0.921
beta2_pH[10,1] 0.618 0.300 0.281 0.560 1.349
beta2_pH[11,1] 0.786 0.205 0.485 0.756 1.284
beta2_pH[12,1] 1.350 0.489 0.726 1.259 2.583
beta2_pH[13,1] 0.742 0.219 0.415 0.709 1.259
beta2_pH[14,1] 0.835 0.211 0.528 0.800 1.350
beta2_pH[15,1] 0.807 0.286 0.419 0.756 1.514
beta2_pH[16,1] 0.384 0.174 0.176 0.336 0.838
beta2_pH[1,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[2,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,2] -2.419 9.876 -21.135 -2.831 18.237
beta2_pH[4,2] -2.244 9.919 -21.165 -2.639 18.471
beta2_pH[5,2] -2.096 10.170 -21.487 -2.345 18.737
beta2_pH[6,2] -2.073 10.310 -21.572 -2.572 18.637
beta2_pH[7,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[8,2] -2.154 10.240 -21.967 -2.472 18.143
beta2_pH[9,2] -2.296 10.288 -21.664 -2.859 18.651
beta2_pH[10,2] 0.000 0.000 0.000 0.000 0.000
beta2_pH[11,2] -8.713 3.402 -17.148 -8.102 -3.993
beta2_pH[12,2] -6.726 3.903 -15.005 -6.416 -0.931
beta2_pH[13,2] -6.611 3.925 -16.013 -5.895 -1.588
beta2_pH[14,2] -7.241 3.466 -15.515 -6.666 -2.528
beta2_pH[15,2] -8.494 3.543 -16.944 -7.723 -3.637
beta2_pH[16,2] -8.835 3.614 -17.825 -8.103 -3.915
beta2_pH[1,3] 5.311 6.094 0.160 3.072 21.251
beta2_pH[2,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[3,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[4,3] 0.000 0.000 0.000 0.000 0.000
beta2_pH[5,3] 7.325 5.731 0.179 6.292 20.897
beta2_pH[6,3] 7.309 5.806 0.078 6.205 21.787
beta2_pH[7,3] 6.817 5.811 0.549 5.218 21.706
beta2_pH[8,3] 8.361 5.242 1.101 7.401 21.486
beta2_pH[9,3] 6.970 5.882 0.340 5.729 21.136
beta2_pH[10,3] 6.321 6.001 0.346 4.891 21.177
beta2_pH[11,3] -2.239 1.823 -7.447 -1.708 -0.654
beta2_pH[12,3] -2.309 1.633 -6.580 -1.851 -0.964
beta2_pH[13,3] -2.806 2.115 -9.007 -2.152 -0.777
beta2_pH[14,3] -2.763 2.017 -8.466 -2.132 -0.936
beta2_pH[15,3] -2.997 2.111 -9.089 -2.299 -1.047
beta2_pH[16,3] -2.929 2.120 -8.757 -2.228 -0.917
beta3_pH[1,1] 35.802 0.819 34.171 35.799 37.408
beta3_pH[2,1] 33.591 1.143 31.644 33.487 36.037
beta3_pH[3,1] 33.647 1.044 31.649 33.624 35.779
beta3_pH[4,1] 33.827 1.203 31.650 33.760 36.344
beta3_pH[5,1] 27.751 1.147 26.508 27.495 31.038
beta3_pH[6,1] 38.657 3.156 32.728 38.579 44.964
beta3_pH[7,1] 30.728 7.995 18.541 30.163 45.151
beta3_pH[8,1] 39.739 2.028 36.037 39.567 44.429
beta3_pH[9,1] 30.792 1.591 28.145 30.668 34.168
beta3_pH[10,1] 32.903 0.946 31.176 32.833 34.909
beta3_pH[11,1] 30.329 0.464 29.433 30.327 31.242
beta3_pH[12,1] 30.156 0.410 29.342 30.157 30.958
beta3_pH[13,1] 33.175 0.581 32.092 33.163 34.315
beta3_pH[14,1] 32.018 0.453 31.159 31.995 32.957
beta3_pH[15,1] 31.200 0.676 29.865 31.183 32.583
beta3_pH[16,1] 32.015 1.018 30.369 31.894 34.461
beta3_pH[1,2] 30.096 7.975 18.476 29.022 45.002
beta3_pH[2,2] 30.002 8.067 18.401 28.921 45.131
beta3_pH[3,2] 31.580 8.335 18.652 31.312 44.881
beta3_pH[4,2] 29.943 7.994 18.386 29.029 44.708
beta3_pH[5,2] 30.045 7.889 18.546 29.137 44.860
beta3_pH[6,2] 29.973 7.876 18.558 29.046 45.018
beta3_pH[7,2] 30.004 7.913 18.546 29.215 44.842
beta3_pH[8,2] 29.837 7.964 18.497 28.732 44.754
beta3_pH[9,2] 29.854 7.971 18.371 28.848 44.771
beta3_pH[10,2] 30.220 7.978 18.577 29.332 45.121
beta3_pH[11,2] 43.403 0.177 43.123 43.383 43.781
beta3_pH[12,2] 43.187 0.185 42.856 43.154 43.670
beta3_pH[13,2] 43.859 0.150 43.471 43.894 44.062
beta3_pH[14,2] 43.311 0.194 43.059 43.265 43.781
beta3_pH[15,2] 43.409 0.190 43.108 43.387 43.806
beta3_pH[16,2] 43.502 0.185 43.174 43.502 43.849
beta3_pH[1,3] 39.176 2.041 34.462 39.767 42.205
beta3_pH[2,3] 30.209 8.064 18.556 29.354 44.911
beta3_pH[3,3] 30.067 8.002 18.448 29.045 44.834
beta3_pH[4,3] 30.493 7.951 18.534 29.879 44.726
beta3_pH[5,3] 27.079 6.835 18.370 25.753 43.072
beta3_pH[6,3] 27.692 6.420 18.769 25.789 44.019
beta3_pH[7,3] 26.602 1.048 24.983 26.426 28.971
beta3_pH[8,3] 41.496 0.288 41.009 41.491 41.961
beta3_pH[9,3] 32.888 1.675 27.228 33.451 34.236
beta3_pH[10,3] 35.432 1.310 32.059 35.964 36.842
beta3_pH[11,3] 41.709 0.818 40.006 41.749 43.213
beta3_pH[12,3] 41.723 0.387 40.942 41.738 42.474
beta3_pH[13,3] 42.741 0.856 41.153 42.769 44.533
beta3_pH[14,3] 41.076 0.560 39.905 41.097 42.099
beta3_pH[15,3] 42.682 0.637 41.263 42.781 43.711
beta3_pH[16,3] 42.907 0.709 41.307 43.004 44.106
beta0_pelagic[1] 2.207 0.130 1.947 2.206 2.465
beta0_pelagic[2] 1.516 0.120 1.285 1.514 1.755
beta0_pelagic[3] -0.152 0.496 -1.124 -0.061 0.587
beta0_pelagic[4] -0.206 0.692 -1.836 -0.036 0.752
beta0_pelagic[5] 1.176 0.255 0.658 1.181 1.659
beta0_pelagic[6] 1.466 0.273 0.873 1.490 1.953
beta0_pelagic[7] 1.645 0.221 1.253 1.628 2.128
beta0_pelagic[8] 1.757 0.198 1.381 1.749 2.189
beta0_pelagic[9] 2.493 0.318 1.859 2.492 3.069
beta0_pelagic[10] 2.496 0.210 2.015 2.512 2.872
beta0_pelagic[11] 0.043 0.472 -1.106 0.080 0.725
beta0_pelagic[12] 1.685 0.140 1.402 1.686 1.960
beta0_pelagic[13] 0.325 0.190 -0.066 0.333 0.675
beta0_pelagic[14] -0.108 0.281 -0.745 -0.080 0.360
beta0_pelagic[15] -0.250 0.135 -0.516 -0.252 0.019
beta0_pelagic[16] 0.342 0.238 -0.325 0.387 0.670
beta1_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta1_pelagic[3] 1.427 0.644 0.438 1.347 2.523
beta1_pelagic[4] 1.508 0.948 0.461 1.253 3.639
beta1_pelagic[5] -0.089 0.319 -0.704 -0.088 0.536
beta1_pelagic[6] -0.091 0.469 -0.869 -0.148 0.788
beta1_pelagic[7] -0.016 0.316 -0.627 -0.025 0.614
beta1_pelagic[8] -0.001 0.277 -0.540 0.001 0.543
beta1_pelagic[9] 0.221 0.483 -0.745 0.347 0.959
beta1_pelagic[10] 0.068 0.274 -0.483 0.066 0.632
beta1_pelagic[11] 3.825 1.187 2.164 3.718 6.550
beta1_pelagic[12] 2.783 0.301 2.179 2.785 3.381
beta1_pelagic[13] 2.874 0.724 1.764 2.768 4.576
beta1_pelagic[14] 4.390 1.068 2.849 4.210 6.763
beta1_pelagic[15] 2.919 0.247 2.455 2.916 3.409
beta1_pelagic[16] 3.441 0.763 2.706 3.235 5.828
beta2_pelagic[1] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[2] 0.000 0.000 0.000 0.000 0.000
beta2_pelagic[3] 1.125 1.854 0.067 0.269 6.757
beta2_pelagic[4] 1.394 1.866 0.049 0.647 6.965
beta2_pelagic[5] -0.007 0.672 -1.418 0.001 1.429
beta2_pelagic[6] -0.091 0.697 -1.481 -0.155 1.322
beta2_pelagic[7] 0.006 0.672 -1.397 0.016 1.402
beta2_pelagic[8] -0.012 0.650 -1.430 -0.016 1.404
beta2_pelagic[9] 0.214 0.684 -1.278 0.271 1.563
beta2_pelagic[10] 0.031 0.637 -1.358 0.040 1.350
beta2_pelagic[11] 1.998 4.065 0.108 0.247 14.606
beta2_pelagic[12] 7.202 5.657 1.421 5.517 22.597
beta2_pelagic[13] 1.057 2.159 0.201 0.480 7.259
beta2_pelagic[14] 0.313 0.139 0.152 0.284 0.633
beta2_pelagic[15] 7.191 5.153 1.671 5.678 21.063
beta2_pelagic[16] 5.981 5.816 0.216 4.685 21.679
beta3_pelagic[1] 29.688 7.773 18.450 28.606 44.783
beta3_pelagic[2] 29.864 7.770 18.573 28.969 44.706
beta3_pelagic[3] 29.217 5.508 20.229 28.861 43.123
beta3_pelagic[4] 24.814 3.890 19.234 24.469 36.881
beta3_pelagic[5] 30.209 8.293 18.473 28.878 45.295
beta3_pelagic[6] 32.065 6.547 19.043 32.175 43.904
beta3_pelagic[7] 29.328 7.665 18.468 28.516 44.754
beta3_pelagic[8] 29.437 7.852 18.391 27.969 44.866
beta3_pelagic[9] 30.924 6.067 19.198 30.970 43.142
beta3_pelagic[10] 29.578 8.084 18.431 28.163 45.023
beta3_pelagic[11] 42.675 1.588 39.024 43.024 45.522
beta3_pelagic[12] 43.455 0.249 43.038 43.445 43.914
beta3_pelagic[13] 42.829 1.259 40.418 42.770 45.519
beta3_pelagic[14] 42.424 1.723 38.931 42.397 45.612
beta3_pelagic[15] 43.213 0.224 42.762 43.193 43.672
beta3_pelagic[16] 43.166 0.640 41.572 43.225 44.279
mu_beta0_pelagic[1] 0.791 0.954 -1.265 0.840 2.634
mu_beta0_pelagic[2] 1.806 0.366 1.057 1.811 2.521
mu_beta0_pelagic[3] 0.334 0.473 -0.635 0.341 1.225
tau_beta0_pelagic[1] 0.565 0.566 0.052 0.376 2.114
tau_beta0_pelagic[2] 2.765 2.876 0.288 2.012 9.996
tau_beta0_pelagic[3] 1.581 1.235 0.184 1.270 4.898
beta0_yellow[1] -0.558 0.230 -1.149 -0.524 -0.230
beta0_yellow[2] 0.432 0.315 -0.072 0.474 0.773
beta0_yellow[3] -0.306 0.216 -0.787 -0.295 0.066
beta0_yellow[4] 0.722 0.388 -0.385 0.822 1.182
beta0_yellow[5] -1.266 0.421 -2.121 -1.258 -0.445
beta0_yellow[6] 0.270 0.216 -0.147 0.263 0.712
beta0_yellow[7] 0.984 0.379 -0.322 1.042 1.334
beta0_yellow[8] 0.695 0.684 -1.352 0.932 1.269
beta0_yellow[9] -0.142 0.303 -0.685 -0.135 0.383
beta0_yellow[10] 0.234 0.151 -0.064 0.231 0.527
beta0_yellow[11] -2.051 0.437 -2.906 -2.045 -1.176
beta0_yellow[12] -3.688 0.416 -4.599 -3.671 -2.926
beta0_yellow[13] -3.766 0.468 -4.766 -3.725 -2.915
beta0_yellow[14] -2.219 0.498 -3.163 -2.238 -1.222
beta0_yellow[15] -2.942 0.394 -3.744 -2.920 -2.209
beta0_yellow[16] -2.459 0.442 -3.320 -2.466 -1.581
beta1_yellow[1] 0.424 0.683 0.000 0.190 1.837
beta1_yellow[2] 1.254 0.708 0.596 1.104 3.123
beta1_yellow[3] 0.667 0.353 0.001 0.663 1.364
beta1_yellow[4] 1.720 1.043 0.692 1.335 4.593
beta1_yellow[5] 3.239 2.454 1.512 2.939 6.764
beta1_yellow[6] 2.289 0.352 1.603 2.286 2.985
beta1_yellow[7] 7.726 10.948 1.344 4.618 33.401
beta1_yellow[8] 2.780 6.188 0.016 1.855 14.400
beta1_yellow[9] 1.627 0.503 0.883 1.592 2.694
beta1_yellow[10] 2.419 0.494 1.564 2.386 3.492
beta1_yellow[11] 2.196 0.432 1.351 2.195 3.040
beta1_yellow[12] 2.492 0.424 1.714 2.466 3.410
beta1_yellow[13] 2.886 0.472 2.074 2.847 3.917
beta1_yellow[14] 2.287 0.482 1.270 2.301 3.206
beta1_yellow[15] 2.187 0.387 1.477 2.159 2.993
beta1_yellow[16] 2.218 0.435 1.323 2.225 3.087
beta2_yellow[1] -0.674 2.695 -7.065 -0.512 4.052
beta2_yellow[2] -1.669 1.828 -6.409 -1.025 -0.100
beta2_yellow[3] -1.635 1.909 -7.046 -1.047 0.897
beta2_yellow[4] -1.523 1.998 -7.296 -0.672 -0.072
beta2_yellow[5] -4.417 2.831 -11.121 -3.941 -0.519
beta2_yellow[6] 3.552 2.189 0.920 2.977 9.298
beta2_yellow[7] -4.577 3.151 -11.587 -4.165 1.572
beta2_yellow[8] -2.165 3.985 -10.185 -2.037 6.554
beta2_yellow[9] 3.716 2.561 0.223 3.329 9.938
beta2_yellow[10] -4.658 2.832 -11.465 -4.101 -0.773
beta2_yellow[11] -3.748 2.094 -9.007 -3.290 -1.144
beta2_yellow[12] -4.057 2.108 -9.090 -3.648 -1.376
beta2_yellow[13] -3.946 1.926 -8.651 -3.528 -1.471
beta2_yellow[14] -3.882 2.010 -8.658 -3.529 -0.988
beta2_yellow[15] -3.590 1.947 -8.496 -3.139 -1.087
beta2_yellow[16] -4.067 2.045 -9.382 -3.669 -1.349
beta3_yellow[1] 27.591 7.557 18.268 25.613 44.383
beta3_yellow[2] 29.014 2.607 22.237 29.034 33.669
beta3_yellow[3] 32.824 3.945 22.264 32.861 41.700
beta3_yellow[4] 28.747 4.081 19.829 28.105 36.753
beta3_yellow[5] 33.320 1.497 30.034 33.392 35.474
beta3_yellow[6] 39.687 0.558 38.727 39.637 40.980
beta3_yellow[7] 20.198 2.019 18.442 19.959 26.213
beta3_yellow[8] 25.118 5.689 18.275 24.153 42.190
beta3_yellow[9] 37.550 2.356 35.544 37.584 42.335
beta3_yellow[10] 29.312 0.601 27.804 29.393 30.073
beta3_yellow[11] 45.349 0.507 44.079 45.452 45.966
beta3_yellow[12] 43.316 0.381 42.581 43.294 44.093
beta3_yellow[13] 44.854 0.380 44.022 44.915 45.510
beta3_yellow[14] 44.270 1.210 43.091 44.299 45.794
beta3_yellow[15] 45.236 0.513 44.175 45.243 45.971
beta3_yellow[16] 44.587 0.623 43.462 44.561 45.799
mu_beta0_yellow[1] 0.055 0.560 -1.154 0.066 1.213
mu_beta0_yellow[2] 0.124 0.482 -0.875 0.146 1.051
mu_beta0_yellow[3] -2.523 0.622 -3.457 -2.607 -0.984
tau_beta0_yellow[1] 2.156 3.704 0.093 1.249 8.711
tau_beta0_yellow[2] 1.220 1.058 0.142 0.941 3.915
tau_beta0_yellow[3] 1.489 2.083 0.111 0.974 5.607
beta0_black[1] -0.089 0.151 -0.389 -0.088 0.199
beta0_black[2] 1.917 0.126 1.670 1.918 2.160
beta0_black[3] 1.317 0.131 1.061 1.317 1.583
beta0_black[4] 2.426 0.129 2.166 2.426 2.679
beta0_black[5] 1.691 1.912 -2.252 1.712 5.876
beta0_black[6] 1.663 1.916 -2.341 1.664 5.613
beta0_black[7] 1.606 1.953 -2.602 1.649 5.607
beta0_black[8] 1.287 0.219 0.873 1.289 1.716
beta0_black[9] 2.443 0.242 1.969 2.444 2.919
beta0_black[10] 1.468 0.132 1.214 1.465 1.731
beta0_black[11] 3.482 0.148 3.197 3.480 3.780
beta0_black[12] 4.853 0.170 4.529 4.854 5.182
beta0_black[13] -0.177 0.250 -0.713 -0.160 0.278
beta0_black[14] 2.853 0.154 2.541 2.854 3.151
beta0_black[15] 1.291 0.149 0.998 1.290 1.591
beta0_black[16] 4.277 0.156 3.979 4.275 4.585
beta2_black[1] 3.478 2.265 0.764 2.889 9.494
beta2_black[2] 0.000 0.000 0.000 0.000 0.000
beta2_black[3] 0.000 0.000 0.000 0.000 0.000
beta2_black[4] 0.000 0.000 0.000 0.000 0.000
beta2_black[5] 0.000 0.000 0.000 0.000 0.000
beta2_black[6] 0.000 0.000 0.000 0.000 0.000
beta2_black[7] 0.000 0.000 0.000 0.000 0.000
beta2_black[8] 0.000 0.000 0.000 0.000 0.000
beta2_black[9] 0.000 0.000 0.000 0.000 0.000
beta2_black[10] 0.000 0.000 0.000 0.000 0.000
beta2_black[11] 0.000 0.000 0.000 0.000 0.000
beta2_black[12] 0.000 0.000 0.000 0.000 0.000
beta2_black[13] -1.799 1.609 -6.222 -1.294 -0.290
beta2_black[14] 0.000 0.000 0.000 0.000 0.000
beta2_black[15] 0.000 0.000 0.000 0.000 0.000
beta2_black[16] 0.000 0.000 0.000 0.000 0.000
beta3_black[1] 41.781 0.853 40.054 41.914 43.066
beta3_black[2] 25.000 0.000 25.000 25.000 25.000
beta3_black[3] 25.000 0.000 25.000 25.000 25.000
beta3_black[4] 25.000 0.000 25.000 25.000 25.000
beta3_black[5] 25.000 0.000 25.000 25.000 25.000
beta3_black[6] 25.000 0.000 25.000 25.000 25.000
beta3_black[7] 25.000 0.000 25.000 25.000 25.000
beta3_black[8] 25.000 0.000 25.000 25.000 25.000
beta3_black[9] 25.000 0.000 25.000 25.000 25.000
beta3_black[10] 25.000 0.000 25.000 25.000 25.000
beta3_black[11] 25.000 0.000 25.000 25.000 25.000
beta3_black[12] 25.000 0.000 25.000 25.000 25.000
beta3_black[13] 39.169 0.931 36.974 39.319 40.511
beta3_black[14] 25.000 0.000 25.000 25.000 25.000
beta3_black[15] 25.000 0.000 25.000 25.000 25.000
beta3_black[16] 25.000 0.000 25.000 25.000 25.000
beta4_black[1] -0.256 0.190 -0.626 -0.263 0.122
beta4_black[2] 0.238 0.177 -0.102 0.240 0.585
beta4_black[3] -0.937 0.189 -1.321 -0.937 -0.567
beta4_black[4] 0.417 0.210 0.007 0.412 0.830
beta4_black[5] 0.216 2.421 -4.363 0.170 5.221
beta4_black[6] 0.186 2.453 -4.738 0.137 5.181
beta4_black[7] 0.322 2.429 -4.221 0.171 5.702
beta4_black[8] -0.693 0.369 -1.406 -0.692 0.007
beta4_black[9] 1.454 1.017 -0.069 1.292 3.852
beta4_black[10] 0.030 0.186 -0.328 0.030 0.398
beta4_black[11] -0.693 0.206 -1.093 -0.692 -0.293
beta4_black[12] 0.168 0.317 -0.427 0.165 0.809
beta4_black[13] -1.188 0.218 -1.625 -1.189 -0.762
beta4_black[14] -0.188 0.229 -0.625 -0.188 0.281
beta4_black[15] -0.890 0.208 -1.314 -0.890 -0.493
beta4_black[16] -0.604 0.223 -1.050 -0.604 -0.176
mu_beta0_black[1] 1.283 0.927 -0.782 1.328 2.993
mu_beta0_black[2] 1.607 0.912 -0.641 1.660 3.383
mu_beta0_black[3] 2.514 0.994 0.382 2.556 4.401
tau_beta0_black[1] 0.623 0.588 0.059 0.453 2.155
tau_beta0_black[2] 1.920 3.795 0.058 0.835 9.943
tau_beta0_black[3] 0.232 0.158 0.049 0.194 0.639
beta0_dsr[11] -2.895 0.280 -3.456 -2.893 -2.352
beta0_dsr[12] 4.519 0.277 3.982 4.516 5.062
beta0_dsr[13] -1.334 0.284 -1.897 -1.335 -0.779
beta0_dsr[14] -3.640 0.492 -4.627 -3.630 -2.702
beta0_dsr[15] -1.936 0.268 -2.483 -1.938 -1.426
beta0_dsr[16] -2.977 0.357 -3.700 -2.971 -2.303
beta1_dsr[11] 4.830 0.298 4.259 4.823 5.421
beta1_dsr[12] 6.623 8.569 2.312 5.017 19.584
beta1_dsr[13] 2.842 0.297 2.299 2.834 3.432
beta1_dsr[14] 6.300 0.515 5.325 6.290 7.331
beta1_dsr[15] 3.329 0.271 2.819 3.325 3.883
beta1_dsr[16] 5.799 0.376 5.084 5.788 6.572
beta2_dsr[11] -8.265 2.283 -13.549 -7.946 -4.611
beta2_dsr[12] -7.113 2.620 -12.994 -6.915 -2.506
beta2_dsr[13] -6.680 2.794 -12.839 -6.552 -1.797
beta2_dsr[14] -6.214 2.687 -11.900 -6.080 -1.789
beta2_dsr[15] -7.765 2.330 -13.208 -7.485 -4.002
beta2_dsr[16] -7.991 2.364 -13.542 -7.692 -4.362
beta3_dsr[11] 43.488 0.144 43.221 43.488 43.769
beta3_dsr[12] 33.988 0.736 32.101 34.130 34.790
beta3_dsr[13] 43.243 0.264 42.856 43.185 43.829
beta3_dsr[14] 43.335 0.226 43.075 43.272 43.902
beta3_dsr[15] 43.504 0.186 43.168 43.500 43.847
beta3_dsr[16] 43.438 0.159 43.166 43.427 43.752
beta4_dsr[11] 0.584 0.208 0.177 0.581 0.988
beta4_dsr[12] 0.254 0.432 -0.578 0.252 1.127
beta4_dsr[13] -0.170 0.210 -0.575 -0.172 0.233
beta4_dsr[14] 0.152 0.245 -0.342 0.154 0.625
beta4_dsr[15] 0.729 0.208 0.319 0.729 1.138
beta4_dsr[16] 0.137 0.224 -0.311 0.142 0.567
beta0_slope[11] -1.941 0.162 -2.255 -1.942 -1.617
beta0_slope[12] -4.658 0.268 -5.199 -4.650 -4.165
beta0_slope[13] -1.334 0.202 -1.755 -1.322 -0.971
beta0_slope[14] -2.641 0.175 -2.991 -2.641 -2.302
beta0_slope[15] -1.372 0.163 -1.696 -1.371 -1.050
beta0_slope[16] -2.719 0.168 -3.061 -2.717 -2.382
beta1_slope[11] 4.596 0.296 4.021 4.591 5.167
beta1_slope[12] 5.013 0.525 4.031 5.002 6.084
beta1_slope[13] 2.908 0.483 2.240 2.850 4.147
beta1_slope[14] 6.527 0.547 5.504 6.513 7.623
beta1_slope[15] 3.046 0.282 2.497 3.049 3.613
beta1_slope[16] 5.374 0.398 4.603 5.365 6.167
beta2_slope[11] 8.068 2.360 4.467 7.713 13.534
beta2_slope[12] 7.142 2.550 2.616 6.884 12.880
beta2_slope[13] 5.845 2.974 0.454 5.856 12.014
beta2_slope[14] 6.514 2.429 2.452 6.343 11.800
beta2_slope[15] 7.493 2.387 3.650 7.169 12.951
beta2_slope[16] 7.591 2.392 3.970 7.207 13.241
beta3_slope[11] 43.473 0.151 43.202 43.471 43.767
beta3_slope[12] 43.405 0.229 43.058 43.379 43.866
beta3_slope[13] 43.635 0.438 42.920 43.713 44.275
beta3_slope[14] 43.317 0.174 43.095 43.281 43.782
beta3_slope[15] 43.515 0.195 43.151 43.515 43.871
beta3_slope[16] 43.461 0.168 43.173 43.448 43.795
beta4_slope[11] -0.579 0.217 -1.004 -0.580 -0.150
beta4_slope[12] -1.422 0.660 -2.952 -1.331 -0.380
beta4_slope[13] 0.047 0.218 -0.371 0.045 0.483
beta4_slope[14] -0.173 0.256 -0.661 -0.179 0.354
beta4_slope[15] -0.727 0.213 -1.144 -0.725 -0.316
beta4_slope[16] -0.201 0.229 -0.651 -0.196 0.245
sigma_H[1] 0.202 0.054 0.107 0.199 0.322
sigma_H[2] 0.172 0.030 0.120 0.170 0.234
sigma_H[3] 0.196 0.043 0.117 0.193 0.288
sigma_H[4] 0.422 0.079 0.292 0.412 0.602
sigma_H[5] 0.998 0.208 0.615 0.986 1.433
sigma_H[6] 0.412 0.198 0.047 0.408 0.809
sigma_H[7] 0.307 0.061 0.210 0.298 0.444
sigma_H[8] 0.415 0.084 0.280 0.405 0.598
sigma_H[9] 0.530 0.128 0.335 0.513 0.821
sigma_H[10] 0.208 0.042 0.136 0.205 0.303
sigma_H[11] 0.278 0.047 0.201 0.274 0.379
sigma_H[12] 0.434 0.164 0.205 0.407 0.769
sigma_H[13] 0.214 0.037 0.150 0.212 0.294
sigma_H[14] 0.510 0.092 0.349 0.502 0.706
sigma_H[15] 0.247 0.040 0.181 0.243 0.337
sigma_H[16] 0.222 0.042 0.152 0.218 0.316
lambda_H[1] 2.988 3.830 0.164 1.734 13.987
lambda_H[2] 8.308 7.906 0.762 6.075 29.007
lambda_H[3] 6.068 9.167 0.288 3.111 29.146
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 3.927 9.469 0.035 1.007 28.024
lambda_H[6] 7.827 15.302 0.008 1.101 49.683
lambda_H[7] 0.013 0.009 0.002 0.010 0.036
lambda_H[8] 8.233 10.321 0.111 4.821 37.194
lambda_H[9] 0.015 0.010 0.003 0.013 0.038
lambda_H[10] 0.275 0.349 0.034 0.191 0.956
lambda_H[11] 0.264 0.401 0.011 0.129 1.247
lambda_H[12] 4.769 6.053 0.202 2.764 22.940
lambda_H[13] 3.519 3.288 0.226 2.586 11.964
lambda_H[14] 3.365 4.937 0.210 2.038 13.367
lambda_H[15] 0.025 0.038 0.003 0.017 0.104
lambda_H[16] 0.796 1.125 0.041 0.417 3.636
mu_lambda_H[1] 4.336 1.961 1.154 4.126 8.622
mu_lambda_H[2] 3.883 1.937 0.624 3.718 7.923
mu_lambda_H[3] 3.468 1.825 0.802 3.162 7.653
sigma_lambda_H[1] 8.638 4.461 1.939 7.870 18.559
sigma_lambda_H[2] 8.549 4.655 1.117 8.054 18.478
sigma_lambda_H[3] 6.231 3.948 1.007 5.365 15.979
beta_H[1,1] 6.873 1.070 4.376 7.048 8.558
beta_H[2,1] 9.882 0.500 8.752 9.909 10.779
beta_H[3,1] 7.985 0.811 6.060 8.087 9.300
beta_H[4,1] 9.531 7.896 -6.991 9.756 24.710
beta_H[5,1] 0.194 2.261 -4.391 0.297 4.186
beta_H[6,1] 3.192 4.004 -7.251 4.612 7.822
beta_H[7,1] 0.342 5.841 -12.194 0.791 10.814
beta_H[8,1] 1.415 4.051 -2.276 1.266 3.529
beta_H[9,1] 12.996 5.728 1.679 13.015 24.523
beta_H[10,1] 7.065 1.705 3.599 7.116 10.497
beta_H[11,1] 5.076 3.547 -2.876 5.824 10.020
beta_H[12,1] 2.574 0.993 0.727 2.520 4.717
beta_H[13,1] 9.066 0.956 7.172 9.165 10.527
beta_H[14,1] 2.171 1.079 0.062 2.185 4.305
beta_H[15,1] -6.119 3.847 -13.176 -6.378 1.956
beta_H[16,1] 3.474 2.649 -0.810 3.177 9.565
beta_H[1,2] 7.904 0.246 7.391 7.911 8.344
beta_H[2,2] 10.025 0.135 9.749 10.024 10.287
beta_H[3,2] 8.948 0.196 8.574 8.945 9.335
beta_H[4,2] 3.573 1.472 0.932 3.517 6.583
beta_H[5,2] 1.994 0.942 0.102 1.995 3.782
beta_H[6,2] 5.739 1.048 3.264 5.901 7.289
beta_H[7,2] 2.693 1.113 0.660 2.610 5.036
beta_H[8,2] 3.009 1.090 1.386 3.149 4.247
beta_H[9,2] 3.493 1.115 1.355 3.470 5.758
beta_H[10,2] 8.199 0.344 7.497 8.211 8.844
beta_H[11,2] 9.779 0.636 8.832 9.647 11.207
beta_H[12,2] 3.945 0.372 3.239 3.929 4.705
beta_H[13,2] 9.125 0.252 8.676 9.114 9.637
beta_H[14,2] 4.019 0.367 3.307 4.015 4.754
beta_H[15,2] 11.364 0.692 9.872 11.407 12.609
beta_H[16,2] 4.511 0.786 3.045 4.490 6.151
beta_H[1,3] 8.465 0.244 8.021 8.450 8.970
beta_H[2,3] 10.064 0.117 9.837 10.063 10.293
beta_H[3,3] 9.623 0.166 9.312 9.615 9.964
beta_H[4,3] -2.535 0.874 -4.263 -2.515 -0.893
beta_H[5,3] 3.861 0.608 2.586 3.855 5.029
beta_H[6,3] 7.985 1.187 6.387 7.608 10.540
beta_H[7,3] -2.832 0.647 -4.200 -2.827 -1.590
beta_H[8,3] 5.246 0.506 4.643 5.184 6.318
beta_H[9,3] -2.867 0.743 -4.315 -2.851 -1.472
beta_H[10,3] 8.686 0.279 8.158 8.681 9.252
beta_H[11,3] 8.535 0.288 7.902 8.557 9.032
beta_H[12,3] 5.259 0.312 4.530 5.299 5.775
beta_H[13,3] 8.839 0.177 8.468 8.844 9.172
beta_H[14,3] 5.713 0.277 5.112 5.735 6.195
beta_H[15,3] 10.369 0.322 9.750 10.357 11.014
beta_H[16,3] 6.235 0.581 4.991 6.286 7.212
beta_H[1,4] 8.254 0.175 7.878 8.263 8.578
beta_H[2,4] 10.130 0.121 9.867 10.139 10.350
beta_H[3,4] 10.117 0.165 9.762 10.133 10.412
beta_H[4,4] 11.801 0.445 10.922 11.812 12.664
beta_H[5,4] 5.524 0.746 4.311 5.445 7.254
beta_H[6,4] 7.059 0.926 4.963 7.343 8.311
beta_H[7,4] 8.226 0.348 7.535 8.233 8.920
beta_H[8,4] 6.709 0.249 6.247 6.718 7.124
beta_H[9,4] 7.191 0.462 6.288 7.185 8.108
beta_H[10,4] 7.715 0.227 7.285 7.710 8.179
beta_H[11,4] 9.390 0.200 9.010 9.390 9.793
beta_H[12,4] 7.135 0.209 6.735 7.136 7.542
beta_H[13,4] 9.044 0.141 8.756 9.047 9.313
beta_H[14,4] 7.734 0.216 7.322 7.736 8.148
beta_H[15,4] 9.473 0.240 8.999 9.474 9.938
beta_H[16,4] 9.350 0.238 8.927 9.343 9.843
beta_H[1,5] 8.979 0.146 8.679 8.983 9.257
beta_H[2,5] 10.783 0.094 10.602 10.780 10.985
beta_H[3,5] 10.921 0.170 10.615 10.915 11.288
beta_H[4,5] 8.390 0.465 7.478 8.372 9.327
beta_H[5,5] 5.463 0.580 4.043 5.501 6.476
beta_H[6,5] 8.831 0.629 7.939 8.671 10.326
beta_H[7,5] 6.786 0.336 6.136 6.784 7.465
beta_H[8,5] 8.211 0.215 7.854 8.198 8.624
beta_H[9,5] 8.199 0.472 7.250 8.199 9.121
beta_H[10,5] 10.098 0.220 9.671 10.100 10.530
beta_H[11,5] 11.504 0.225 11.049 11.511 11.933
beta_H[12,5] 8.484 0.198 8.100 8.483 8.872
beta_H[13,5] 10.013 0.131 9.755 10.013 10.274
beta_H[14,5] 9.210 0.234 8.784 9.198 9.695
beta_H[15,5] 11.164 0.246 10.681 11.172 11.632
beta_H[16,5] 9.914 0.178 9.546 9.921 10.243
beta_H[1,6] 10.186 0.189 9.863 10.168 10.598
beta_H[2,6] 11.517 0.110 11.304 11.518 11.738
beta_H[3,6] 10.810 0.162 10.456 10.817 11.105
beta_H[4,6] 12.864 0.823 11.257 12.885 14.437
beta_H[5,6] 5.925 0.609 4.766 5.906 7.161
beta_H[6,6] 8.828 0.659 7.042 8.952 9.780
beta_H[7,6] 9.805 0.569 8.675 9.811 10.909
beta_H[8,6] 9.523 0.282 9.001 9.544 9.958
beta_H[9,6] 8.447 0.797 6.938 8.443 10.071
beta_H[10,6] 9.515 0.314 8.831 9.534 10.078
beta_H[11,6] 10.823 0.350 10.085 10.850 11.464
beta_H[12,6] 9.369 0.246 8.895 9.358 9.864
beta_H[13,6] 11.044 0.162 10.757 11.034 11.380
beta_H[14,6] 9.815 0.291 9.230 9.814 10.396
beta_H[15,6] 10.852 0.427 9.998 10.855 11.702
beta_H[16,6] 10.540 0.240 10.044 10.547 11.012
beta_H[1,7] 10.880 0.877 8.797 11.002 12.319
beta_H[2,7] 12.204 0.433 11.312 12.201 13.066
beta_H[3,7] 10.549 0.666 9.068 10.623 11.651
beta_H[4,7] 2.519 4.231 -5.375 2.402 11.280
beta_H[5,7] 6.382 1.814 2.919 6.363 10.183
beta_H[6,7] 9.621 2.400 4.634 9.607 15.997
beta_H[7,7] 10.671 2.903 4.607 10.697 16.300
beta_H[8,7] 10.995 1.053 9.492 10.939 12.746
beta_H[9,7] 4.475 4.114 -3.825 4.511 12.666
beta_H[10,7] 9.820 1.440 7.192 9.721 12.906
beta_H[11,7] 10.958 1.726 7.742 10.842 14.759
beta_H[12,7] 9.984 0.934 7.956 10.079 11.532
beta_H[13,7] 11.665 0.743 9.918 11.754 12.888
beta_H[14,7] 10.396 0.997 8.235 10.446 12.203
beta_H[15,7] 11.915 2.192 7.509 11.936 16.193
beta_H[16,7] 12.263 1.240 10.149 12.149 15.113
beta0_H[1] 8.592 13.419 -18.153 8.754 34.747
beta0_H[2] 10.576 6.512 -1.938 10.590 24.073
beta0_H[3] 9.776 10.469 -11.381 9.918 29.346
beta0_H[4] 8.586 179.960 -358.753 6.201 370.571
beta0_H[5] 4.105 23.355 -42.448 4.243 51.713
beta0_H[6] 8.499 48.374 -101.287 7.680 114.635
beta0_H[7] 6.048 135.752 -268.075 6.120 282.879
beta0_H[8] 6.437 33.769 -17.349 6.449 27.743
beta0_H[9] 3.362 126.739 -260.693 5.828 246.966
beta0_H[10] 7.157 32.342 -63.464 6.825 70.286
beta0_H[11] 10.553 49.877 -97.745 9.999 114.864
beta0_H[12] 7.026 11.215 -15.076 6.761 30.066
beta0_H[13] 10.095 11.173 -8.863 10.069 30.908
beta0_H[14] 7.034 12.281 -16.104 7.104 30.783
beta0_H[15] 7.582 110.851 -217.391 8.829 231.995
beta0_H[16] 7.745 25.325 -45.488 7.923 60.851